It had a decisive impact on twentieth century philosophy and is one of few works to have influenced both continental and analytic philosophy.This is the first time both volumes have been available in paperback. They include a new introduction by Dermot Moran, placing the Investigations in historical context and bringing out their contemporary philosophical importance.These editions include a new preface by Sir Michael Dummett.

    Would you believe that these five pieces can be reassembled in such a fashion so as to create two apples equal in shape and size to the original? Would you believe that you could make something as large as the sun by breaking a pea into a finite number of pieces and putting it back together again? Neither did Leonard Wapner, author of The Pea and the Sun, when he was first introduced to the Banach-Tarski paradox, which asserts exactly such a notion. Written in an engaging style, The Pea and the Sun catalogues the people, events, and mathematics that contributed to the discovery of Banach and Tarski's magical paradox. Wapner makes one of the most interesting problems of advanced mathematics accessible to the non-mathematician.

    His investigations shed light on what we can ultimately know about the universe and the very nature of life. In an infectious and enthusiastic narrative, Chaitin delineates the specific intellectual and intuitive steps he took toward the discovery. He takes us to the very frontiers of scientific thinking, and helps us to appreciate the art—and the sheer beauty—in the science of math.

    Abrams has given us a remarkable study, admirably conceived and executed, a book of quite exceptional and no doubt lasting significance for a number of fields - for the history of ideas and comparative literature as well as for English literary history, criticism and aesthetics.

    The main message i absorbed from it was a set of conditions required for success in mathematics: talent, yes; single-mindedness, almost as obvious; sense of humour, essential when the going gets tough; and love, yes that is the right word - you must love mathematics, and that means all the ingredients, passion, pain and loyalty." The Mathematical Gazette#1"The book is written in a very personal, but plain and honest way, result of reflected experience and mature self-assessment of a wise man. It avoids palliation as well as exaggerated modesty.- It should be a document for history and sociology of science." (R. Fischer) Zentralblatt für Mathematik#2

    More than 40 million students have trusted Schaum's to help them succeed in the classroom and on exams. Schaum's is the key to faster learning and higher grades in every subject. Each Outline presents all the essential course information in an easy-to-follow, topic-by-topic format. You also get hundreds of examples, solved problems, and practice exercises to test your skills. This Schaum's Outline gives you:  Practice problems with full explanations that reinforce knowledge Coverage of the most up-to-date developments in your course field In-depth review of practices and applications Fully compatible with your classroom text, Schaum's highlights all the important facts you need to know. Use Schaum's to shorten your study time-and get your best test scores! Schaum's Outlines-Problem Solved.

    Yet unlike Einstein, with whom he formed a warm and abiding friendship, Gödel has long escaped all but the most casual scrutiny of his life.Stephen Budiansky’s Journey to the Edge of Reason is the first biography to fully draw upon Gödel’s voluminous letters and writings—including a never-before-transcribed shorthand diary of his most intimate thoughts—to explore Gödel’s profound intellectual friendships, his moving relationship with his mother, his troubled yet devoted marriage, and the debilitating bouts of paranoia that ultimately took his life. It also offers an intimate portrait of the scientific and intellectual circles in prewar Vienna, a haunting account of Gödel’s and Jewish intellectuals’ flight from Austria and Germany at the start of the Second World War, and a vivid re-creation of the early days of Princeton’s Institute for Advanced Study, where Gödel and Einstein both worked.Eloquent and insightful, Journey to the Edge of Reason is a fully realized portrait of the odd, brilliant, and tormented man who has been called the greatest logician since Aristotle, and illuminates the far-reaching implications of Gödel’s revolutionary ideas for philosophy, mathematics, artificial intelligence, and man’s place in the cosmos.

    . . Nothing less than a major contribution to the scientific culture of this world." — The New York Times Book ReviewThis major survey of mathematics, featuring the work of 18 outstanding Russian mathematicians and including material on both elementary and advanced levels, encompasses 20 prime subject areas in mathematics in terms of their simple origins and their subsequent sophisticated developement. As Professor Morris Kline of New York University noted, "This unique work presents the amazing panorama of mathematics proper. It is the best answer in print to what mathematics contains both on the elementary and advanced levels."Beginning with an overview and analysis of mathematics, the first of three major divisions of the book progresses to an exploration of analytic geometry, algebra, and ordinary differential equations. The second part introduces partial differential equations, along with theories of curves and surfaces, the calculus of variations, and functions of a complex variable. It furthur examines prime numbers, the theory of probability, approximations, and the role of computers in mathematics. The theory of functions of a real variable opens the final section, followed by discussions of linear algebra and nonEuclidian geometry, topology, functional analysis, and groups and other algebraic systems.Thorough, coherent explanations of each topic are further augumented by numerous illustrative figures, and every chapter concludes with a suggested reading list. Formerly issued as a three-volume set, this mathematical masterpiece is now available in a convenient and modestly priced one-volume edition, perfect for study or reference."This is a masterful English translation of a stupendous and formidable mathematical masterpiece . . ." — Social Science

    In this collection of landmark mathematical works, editor Stephen Hawking has assembled the greatest feats humans have ever accomplished using just numbers and their brains.

    The book has been designed to offer maximal accessibility to the widest range of students (not only those majoring in philosophy) and assumes no formal training in elementary symbolic logic. It offers a comprehensive course covering all basic definitions of induction and probability, and considers such topics as decision theory, Bayesianism, frequency ideas, and the philosophical problem of induction. The key features of the book are: * A lively and vigorous prose style* Lucid and systematic organization and presentation of the ideas* Many practical applications* A rich supply of exercises drawing on examples from such fields as psychology, ecology, economics, bioethics, engineering, and political science* Numerous brief historical accounts of how fundamental ideas of probability and induction developed.* A full bibliography of further reading Although designed primarily for courses in philosophy, the book could certainly be read and enjoyed by those in the social sciences (particularly psychology, economics, political science and sociology) or medical sciences such as epidemiology seeking a reader-friendly account of the basic ideas of probability and induction. Ian Hacking is University Professor, University of Toronto. He is Fellow of the Royal Society of Canada, Fellow of the British Academy, and Fellow of the American Academy of Arts and Sciences. he is author of many books including five previous books with Cambridge (The Logic of Statistical Inference, Why Does Language Matter to Philosophy?, The Emergence of Probability, Representing and Intervening, and The Taming of Chance).

    We wouldn’t have unraveled DNA or discovered Neptune or figured out how to put 5,000 songs in your pocket. Though many of us were scared away from this essential, engrossing subject in high school and college, Steven Strogatz’s brilliantly creative, down‑to‑earth history shows that calculus is not about complexity; it’s about simplicity. It harnesses an unreal number—infinity—to tackle real‑world problems, breaking them down into easier ones and then reassembling the answers into solutions that feel miraculous. Infinite Powers recounts how calculus tantalized and thrilled its inventors, starting with its first glimmers in ancient Greece and bringing us right up to the discovery of gravitational waves (a phenomenon predicted by calculus). Strogatz reveals how this form of math rose to the challenges of each age: how to determine the area of a circle with only sand and a stick; how to explain why Mars goes “backwards” sometimes; how to make electricity with magnets; how to ensure your rocket doesn’t miss the moon; how to turn the tide in the fight against AIDS. As Strogatz proves, calculus is truly the language of the universe. By unveiling the principles of that language, Infinite Powers makes us marvel at the world anew.

    Beginning millions of years ago with ancient “ant odometers” and moving through time to our modern-day quest for new dimensions, it covers 250 milestones in mathematical history. Among the numerous delights readers will learn about as they dip into this inviting anthology: cicada-generated prime numbers, magic squares from centuries ago, the discovery of pi and calculus, and the butterfly effect. Each topic gets a lavishly illustrated spread with stunning color art, along with formulas and concepts, fascinating facts about scientists’ lives, and real-world applications of the theorems.

    Describing experiments that show that human infants have a rudimentary number sense, Stanislas Dehaene suggests that this sense is as basic as our perception of color, and that it is wired into the brain. Dehaene shows that it was the invention of symbolic systems of numerals that started us on the climb to higher mathematics. A fascinating look at the crossroads where numbers and neurons intersect, The Number Sense offers an intriguing tour of how the structure of the brain shapes our mathematical abilities, and how our mathematics opens up a window on the human mind.

    Based on a National Magazine Award-winning article, this masterful biography of Hungarian-born Paul Erdos is both a vivid portrait of an eccentric genius and a layman's guide to some of this century's most startling mathematical discoveries.

    First published in 1954, it details his experiences when taking mescaline. The book takes the form of Huxley's recollection of a mescaline trip that took place over the course of an afternoon in May 1953. The book takes its title from a phrase in William Blake's 1793 poem 'The Marriage of Heaven and Hell'. Huxley recalls the insights he experienced, which range from the "purely aesthetic" to "sacramental vision". He also incorporates later reflections on the experience and its meaning for art and religion.